You will learn
- Put numbers in ascending order.
- Put numbers in descending order.
- Find the smallest and the biggest.
- Check an order.
Version 0.2 · expanded edition · built from cited public sources Content is based on the official frameworks and sources listed under Sources and standards. No official endorsement is claimed. Written in the style of common primary school assessments. No exam result is promised.
Student lesson
- Ascending is smallest to biggest.
- Descending is biggest to smallest.
- Compare the hundreds, then tens, then ones.
- Check your order from end to end.
Words to know
From smallest to biggest.
From biggest to smallest.
Arrange in a line.
The largest number.
1. Discover: race numbers
Four runners have numbers 245, 254, 425 and 452. Line them up from smallest number to biggest. How did you decide?
2. Understand: ordering numbers
To order numbers, compare the hundreds, then the tens, then the ones. Ascending order goes from the smallest to the biggest: 245, 254, 425, 452.
Descending order goes from the biggest to the smallest: 452, 425, 254, 245.
Find the smallest first, cross it out, and repeat.
Idea 1: Ascending
Ascending order goes from smallest to biggest: 245, 254, 425.
Idea 2: Descending
Descending order goes from biggest to smallest: 425, 254, 245.
Idea 3: How to order
Find the smallest first, then the next. Use hundreds, then tens, then ones. Check that each number is bigger than the last.
Why check? One wrong place spoils the whole order.
3. Worked examples
Example 1 (I show you): Ascending
Order 245, 254 and 425 from the smallest.
- Hundreds: 2, 2, 4.
- Tens: 4 and 5.
Answer: 245, 254, 425
Example 2 (We do it together): Biggest
Which is the biggest of 372, 327 and 732?
- Hundreds: 3, 3, 7.
Answer: 732
Example 3 (You try): Descending
Put 505, 550 and 500 in descending order.
Show the steps and answer
- Biggest first: 550.
- Then 505, then 500.
Answer: 550, 505, 500
Did you know?
Race results use descending order of speed. First place is the fastest.
Why this matters
Ordering helps us rank scores and prices.
4. Explore: number line-up
You need 5 number cards.
- Make cards: 372, 327, 732, 237, 723.
- Find the smallest card.
- Line up all cards from smallest to biggest.
- Turn the line around for descending.
Think about it: what did you notice?
Ascending: 237, 327, 372, 723, 732.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- Ascending means ___ to ___.
- Descending means ___ to ___.
- The smallest is ___.
- The biggest is ___.
Guided practice
Question 1. Smallest of 245, 254, 425?
245.
Question 2. Ascending means…
smallest to biggest.
Question 3. Biggest of 372, 327, 732?
732.
Independent practice
Level 1: Start
- Order 245, 254, 425 from smallest.
- Order 372, 327, 732 from biggest.
- Which is the smallest: 505, 550, 500?
- Fill: 100, 200, __ , 400.
- Is 456, 546, 654 ascending?
Level 2: Grow
- Order smallest first: 703, 307, 370.
- Biggest of 450, 540, 405?
- Descending: 150, 510, 105.
Level 3: Stretch
- Three children have 245, 254 and 425 stickers. Who has the most?
- Missing number: 150, __, 350, 450.
- Kofi orders 215, 251, 152 as ascending: 215, 251, 152. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
Three buses carry 120, 98 and 150 pupils. Order them from fewest.
Show a sample answer
98, 120, 150.
Another one. Three buses carry 128, 182 and 218 people. Put the numbers in descending order.
Show a sample answer
218, 182, 128
7. Common mistakes
Fix: Always compare the hundreds first.
Fix: Ascending goes up like stairs. Descending goes down.
Fix: If hundreds match, check the tens.
8. Lesson summary and revision card
- I can put numbers in ascending order.
- I can put numbers in descending order.
- I can find the smallest and biggest.
- I can check an order.
9. Check and master
Answer all 14 questions. You will see feedback after each one.
Your result appears here after you answer every question.
10. Key takeaways
- Compare place by place.
- Ascending goes up, descending goes down.
- Check the order.
11. Next lesson
Next lesson: Number sequences. Keep going with the next idea in this course.
Exam practice
These questions are written in the style of common school and international primary assessments. Try them on your own, without looking back. Then check your answers in the marking guide. The marks are shown in brackets.
- Put in ascending order: 321, 213, 312. [2 marks]
- What is the biggest of 506, 560 and 605? [1 mark]
- Put in descending order: 450, 405, 540. [2 marks]
- Fill the gap: 250, 300, __, 400. [1 mark]
- Ali says 734, 743, 437 is ascending. Is he right? Explain. [2 marks]
Total: 8 marks.
Marking guide and model answers
- 213, 312, 321 [2]. Give 1 mark for one error.
- 605 [1]
- 540, 450, 405 [2]. Give 1 mark for one error.
- 350 [1]
- No [1]. 437 is the smallest and should be first [1].
Score guide: 7 to 8 = secure. 5 to 6 = nearly there, revise the parts you missed. Under 5 = work through the lesson again with a grown-up.
Printable worksheet
- Ascending: 245, 254, 425 …
- Descending: 372, 327, 732 …
- Smallest: 505, 550, 500?
- Fill: 100, 200, __, 400.
- Is 456, 546, 654 ascending?
- Smallest of 303, 330, 300?
- Order 12, 21, 102 from smallest.
- Descending: 201, 120, 210.
- Biggest of 899, 989, 998?
- What does ascending mean?
Homework
Write five three-digit numbers from the doors on your street. Order them.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| Ascending: 245, 254, 425 … | 245, 254, 425 | 2 |
| Descending: 372, 327, 732 … | 732, 372, 327 | 2 |
| Smallest: 505, 550, 500? | 500 | 2 |
| Fill: 100, 200, __, 400. | 300 | 2 |
| Is 456, 546, 654 ascending? | yes | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 245, 254, 425; 2 732, 372, 327; 3 500; 4 300; 5 yes.
Quiz answers: 1 A, 2 B, 3 C, 4 A, 5 B, 6 A, 7 B, 8 C, 9 A, 10 B, 11 C, 12 A, Challenge 1 C, Challenge 2 C.
Extra worksheet answers (items 6 onward): 6 300; 7 12, 21, 102; 8 210, 201, 120; 9 998; 10 Smallest to biggest.
Independent practice answers. Level 1: 1 245, 254, 425; 2 732, 372, 327; 3 500; 4 300; 5 yes. Level 2: 1 307, 370, 703; 2 540; 3 510, 150, 105. Level 3: 1 The child with 425; 2 250; 3 152 is the smallest. It should be first: 152, 215, 251..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Put numbers in ascending order | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
| O2 Put numbers in descending order | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
| O3 Find the smallest and the biggest | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
| O4 Check an order | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
Courseversity badge thresholds (overall quiz score): Gold = 90–100%; Silver = 80–89.9%; Bronze = 70–79.9%. A badge is never a full record of progress.
If a learner struggles
- Find the misconception: Ordering by the last digit. Always compare the hundreds first.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Order only three numbers with different hundreds first.
- Guided practice: work through one example together and let the learner try the next one.
- Reassess: use the quiz again or the worksheet.
- Move on when the learner shows Silver-level evidence independently.
For parents and guardians
In this lesson your child puts three-digit numbers in order from smallest to biggest and back. You do not need to be good at mathematics to help.
- Write three numbers on cards and order them.
- Order the family’s heights or ages.
- Ask: which is the biggest? How do you know?
- Ask “how do you know?” after each answer, and listen.
- Praise effort, not only right answers. Mistakes are how we learn.
- Ten to fifteen minutes a day is better than one long session.
Teacher package
1–5. Objectives, prerequisites, materials, preparation, duration
Lesson objectives. Learners will: put numbers in ascending order; put numbers in descending order; find the smallest and the biggest; check an order.
Prerequisite knowledge. Lesson 6.
Materials. Counters (stones, seeds or bottle tops), paper, pencils, board or chalkboard. Low-resource options: use stones, seeds, sticks, bottle tops or drawings in the sand or on the board instead of printed materials.
Preparation. Gather the counters and draw the example pictures on the board before the lesson.
Suggested duration. 45–60 minutes. It can be split into two shorter sessions.
6–9. Teaching procedure, explanation notes, guided and independent activities
Introduction (5 min). Start with the Discover situation and let learners suggest ideas before you teach.
Explanation (10 min). Teach the Understand section with real objects first, then pictures, then symbols and words.
Guided activity (10 min). You need 5 number cards. Learners follow the Explore steps in pairs.
Independent activity (10 min). Learners complete the independent practice and the worksheet.
Assessment and reflection (5 min). Ask each learner to say one thing they learned and how they know it.
Key questions. Which is smallest? Which is biggest? Is it ascending or descending?
Teacher explanation notes. Use the concrete, pictorial, abstract order: real objects first, then pictures, then symbols and words. Return to real objects whenever a learner needs support.
10–12. Differentiation, formative assessment, common misconceptions
Support. Use real objects and work with a partner; say each step aloud together. Extension. Ask learners to make up their own example and explain it to a partner.
Formative assessment. Listen to learner explanations, ask “how do you know?”, and check the independent work.
Misconceptions. Ordering by the last digit. Always compare the hundreds first.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 8-mark exam practice scheme, the 10-mark scheme and all answers are in the answer sections above. Re-check every answer and the marking scheme before publication.
16–19. Remediation, enrichment, homework, teacher reflection
Remediation. Order only three numbers with different hundreds first. Enrichment. Invite learners to find or create three more examples at home or in the classroom and explain them. Homework. See above.
Teacher reflection. After teaching, record: which concepts learners understood; which misconceptions occurred; which activities worked; which learners need more practice; and what to improve next time.
Sources and standards
This lesson is based on the sources below, and no official endorsement is claimed. Reference starting points named in the Courseversity standard: Common Core State Standards for Mathematics, Cambridge Primary and the IB Primary Years Programme. Where a standard code is named, it points to the official framework.
Official standards for this topic area. Common Core State Standards for Mathematics (official site): Grade 2 » Number & Operations in Base Ten. These pages list the standards that cover this topic area; read them alongside the lesson.
Research used to shape this lesson. Common Core 2.NBT.A.4 (compare and order); Cambridge Primary Mathematics Stage 2. These sources informed the lesson.